The Facebook Mentions app monitors your activity on the social media platform -- if you're a celebrity, that is. Yes, that's right, the app is only available for those who are famous enough to be "verified" on Facebook and other social media outlets.
The app is geared towards more towards users posting their own content, rather than reading what other people have chosen to share. There is a separate feature that curates all the "mentions" the user has accrued, making it easy for them to keep tabs on what the public is saying about them.
For now, the app is only available for public figures; however, in the future, it may expand to regular Joes like you and me.